Correct maintenance for bermuda(high N in summer and a reel cut) normally kills rye. If not many, sulfonylurea herbicides will kill it and other cool season grasses. I know this because it is a common practice here to mix rye with bermuda when seeding big areas. The rye provides a really quick green until the bermuda germinates in 14 days. Personally, I would prefer it not to be done because the rye competes with the bermuda and can shade it out unless it is scalped as soon as the bermuda starts to come up.

Rye does not survive what I do for broadleaf and sedge control. Oddly enough, bermuda does not like what rye will tolerate such as Turflon or Three Way. There are programs using Turflon prior to overseeding rye. Rye is also much more tolerant of the orange herbicides than bermuda is as well.